1. A boy pushes a car to slow it down while the car is rolling horizontally down the road. If the boy pushes backwards on the car with 10N of force as the car rolls forward 3.0m, the amount of work done by the boy is:
a)-30
b)0
c)3.3 J
d)30 N•m
e)300J
my answer: a
2. what is the speed of a 5.0 kg ball if its kinetic energy is 40J?
a)2.8 m/s
b)4 m/s
c)8 m/s
d)16 m/s
e)200 km/h
my answer: b
3. The amount of energy required to raise a 20 kg child onto a counter top that is 1.25 m off the ground is:
(a) 30 J
(b) 0.25 N
(c) 245 J
(d) 30 N
(e) 0 J
my answer: c
4. If mechanical energy is conserved, then
(a) the sum of the kinetic energy and gravitational potential energy remains constant.
(b) the amount of kinetic energy is constant.
(c) thermal energy losses due to friction are constant.
(d) the amount of gravitational potential energy is constant. (e) none of the above.
my answer: a
5. A cyclist on a bike has 4 100 J of energy. If the bicycle and cyclist weigh 82 kg the velocity of the cyclist is:
(a) 100 km/h
(b) 50 km/h
(c) 100 m/s
(d) 10 m/s
(e) 0 m/s
my answer: d
1. Well, if the boy is pushing the car backwards, he's definitely working against the car's motion. So, we can say the work done by the boy is negative. But let's calculate the actual work done. Work is equal to force times distance, so the work done by the boy is 10N * 3.0m = 30N•m. So, the correct answer is d) 30 N•m. That boy sure is working hard!
2. Let's see, if the kinetic energy of the ball is 40J, we can use the formula for kinetic energy: KE = (1/2)mv^2, where KE is kinetic energy, m is mass, and v is velocity. Rearranging the formula, we get v = sqrt(2KE/m). Plugging in the values, we get v = sqrt(2 * 40J / 5.0kg) = sqrt(16m^2/s^2) = 4m/s. So, the correct answer is b) 4 m/s. That's one speedy ball!
3. To raise a child onto a counter top, we need to overcome the force of gravity acting on the child. The potential energy of an object is given by PE = mgh, where PE is potential energy, m is mass, g is acceleration due to gravity, and h is height. Plugging in the values, we get PE = 20kg * 9.8m/s^2 * 1.25m = 245J. So, the correct answer is c) 245 J. That's a lot of energy for a child to get on the counter!
4. When mechanical energy is conserved, it means that the sum of the kinetic energy and gravitational potential energy remains constant. So, the correct answer is a) the sum of the kinetic energy and gravitational potential energy remains constant. Just like how I conserve my energy by not doing any physical work!
5. If the cyclist has 4,100J of energy, it could be a combination of kinetic energy and potential energy. But since there's no mention of any height, let's assume it's all kinetic energy. The formula for kinetic energy is KE = (1/2)mv^2. Rearranging the formula, we get v = sqrt(2KE/m). Plugging in the values, we get v = sqrt(2 * 4,100J / 82kg) = sqrt(100m^2/s^2) = 10m/s. So, the correct answer is d) 10 m/s. That cyclist is on a roll!
1. First, we need to calculate the work done by the boy using the formula: work = force x distance.
Given that the force applied by the boy is 10N and the distance the car is pushed is 3.0m, the work done by the boy is 10N x 3.0m = 30N•m.
Therefore, the correct answer is (d) 30 N•m.
2. The formula to calculate kinetic energy is: kinetic energy = 1/2 x mass x velocity^2.
Given that the mass of the ball is 5.0 kg and the kinetic energy is 40J, we can rearrange the formula to solve for velocity.
40J = 1/2 x 5.0 kg x velocity^2.
Divide both sides by (1/2 x 5.0 kg):
8 = velocity^2.
Taking the square root of both sides:
velocity = √(8) ≈ 2.8 m/s.
Therefore, the correct answer is (a) 2.8 m/s.
3. The amount of energy required to raise an object can be calculated using the formula: energy = force x distance.
Given that the child's mass is 20 kg and the height to raise is 1.25 m, we need to calculate the force first.
Force = mass x acceleration due to gravity = 20 kg x 9.8 m/s^2 ≈ 196 N.
Now, we can calculate the energy:
Energy = force x distance = 196 N x 1.25 m = 245 J.
Therefore, the correct answer is (c) 245 J.
4. When mechanical energy is conserved, the sum of kinetic energy and gravitational potential energy remains constant.
Therefore, the correct answer is (a) the sum of the kinetic energy and gravitational potential energy remains constant.
5. The total energy of the cyclist is given as 4100 J, which is the sum of kinetic energy and gravitational potential energy.
Since gravitational potential energy is not given, we need to calculate it using the formula: gravitational potential energy = mass x acceleration due to gravity x height.
Given that the mass of the cyclist and bicycle is 82 kg and the height is not provided, we cannot determine the gravitational potential energy.
Therefore, we cannot determine the velocity of the cyclist using the given information. The correct answer is (e) 0 m/s.
1. To find the work done by the boy, we need to use the formula: Work = Force * Distance * cosine(theta), where theta is the angle between the direction of the force and the direction of the displacement.
In this case, the boy pushes backwards, so the angle between the force and the displacement is 180 degrees. The force is 10N and the distance is 3.0m.
Work = 10N * 3.0m * cos(180 degrees) = -30J
Therefore, the amount of work done by the boy is -30J. So, the correct answer is a) -30.
2. The kinetic energy (KE) of an object is given by the formula KE = 0.5 * mass * velocity^2.
In this case, the kinetic energy is given as 40J and the mass is 5.0kg. We need to find the velocity of the ball.
Rearranging the formula, we get velocity^2 = (2 * KE) / mass
velocity^2 = (2 * 40J) / 5.0kg
velocity^2 = 80J / 5.0kg
velocity^2 = 16 (J/kg)
Taking the square root of both sides, we get velocity = 4 m/s
Therefore, the speed of the 5.0kg ball is 4 m/s. So, the correct answer is b) 4 m/s.
3. The amount of energy required to raise an object against gravity is given by the formula: Potential energy = mass * gravity * height.
In this case, the mass of the child is 20 kg, the height is 1.25 m, and the acceleration due to gravity is 9.8 m/s^2.
Potential energy = 20 kg * 9.8 m/s^2 * 1.25 m = 245 J
Therefore, the amount of energy required to raise the 20 kg child onto the counter top is 245 J. So, the correct answer is c) 245 J.
4. Mechanical energy is conserved when the sum of the kinetic energy and gravitational potential energy remains constant.
Therefore, the correct answer is a) the sum of the kinetic energy and gravitational potential energy remains constant.
5. The total energy of the cyclist is the sum of the kinetic energy and potential energy due to their position.
Total energy = Kinetic energy + Gravitational potential energy
Given that the kinetic energy is 4 100 J and the combined mass of the bicycle and cyclist is 82 kg, the gravitational potential energy can be calculated using the formula: Potential energy = mass * gravity * height.
Potential energy = 82 kg * 9.8 m/s^2 * 0 m (height is 0 since there is no mention of an elevation change)
Total energy = 4,100 J + 0 J = 4,100 J
Since the total energy is equal to the kinetic energy, we can rearrange the kinetic energy formula to find the velocity:
velocity = square root(2 * total energy / mass)
velocity = square root(2 * 4,100 J / 82 kg)
velocity = square root(50)
velocity ≈ 7.07 m/s
Therefore, the velocity of the cyclist is approximately 7.07 m/s. So, none of the given options are correct.
1. My answer is zero, because the car did not move backwards. However, you should get a 2nd opinion.
2. KE = 0.5*m*V^2 = 40 Joules
KE = 0.5*5*V^2 = 40
2.5V^2 = 40
V^2 = 16
V = 4 m/s.
3c.
4a. PE + KE = Constant
5. I don't know what you mean by 4 100 J
If you mean 400 J. the answer is d.