1) A 20 kg rock is on the edge of a 100 m cliff.
a. What potential energy does the rock possess relative to the base of the cliff?
b. The rock falls from the cliff. What is the kinetic energy just before it strikes the ground?
c. What speed does the rock have as it strikes the ground?
2) Justin pulls his 55 kg girlfriend in a 12 kg sled with a constant force of 79 N for 120 meters.
a. How much work did Justin do moving his girlfriend?
b. How much power did he expend if it took him 4 minutes to move this distance?
1) PE = mgh
PE = 20 kg * 9.8 m/sec^2 *100m
KE = PE
KE = 1/2 * m*v^2
2) W=F x d
F = mg
Force = 55 x 9.8 m/sec^2
1) a. The potential energy of the rock is about to drop to rock bottom! Sorry, I couldn't resist. The potential energy of the rock relative to the base of the cliff can be calculated using the formula PE = mgh, where m is the mass of the rock, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height of the cliff (100 m in this case). Let me do the math for you. PE = 20 kg * 9.8 m/s^2 * 100 m = 19,600 J.
b. As the rock falls from the cliff, it gains kinetic energy. The kinetic energy of an object is calculated using the formula KE = (1/2)mv^2, where m is the mass of the object and v is its velocity. Since the rock falls freely under the influence of gravity, its potential energy is converted entirely into kinetic energy just before it strikes the ground. Therefore, the kinetic energy of the rock just before it strikes the ground is also 19,600 J.
c. To find the speed of the rock as it strikes the ground, we need to use the concept of conservation of energy. The potential energy of the rock is converted completely into kinetic energy. Let's use the formula KE = (1/2)mv^2 to solve for v. Rearranging the formula, we have v = sqrt(2(KE/m)). Substituting the values, v = sqrt(2(19,600 J / 20 kg)) ≈ 31.3 m/s.
2) a. Justin must be quite the strong guy to pull his girlfriend and the sled! The work done by Justin can be calculated using the formula W = Fd, where W is the work done, F is the force applied, and d is the distance moved. Plugging in the values, we get W = 79 N * 120 m = 9,480 J.
b. Moving on to power, we can calculate it using the formula P = W/t, where P is power, W is the work done, and t is the time taken. Converting 4 minutes into seconds (since power is measured in watts, which is joules per second), we have t = 4 min * 60 s/min = 240 s. Plugging in the values, P = 9,480 J / 240 s ≈ 39.5 W.
Hope that brings a smile to your face!
1) First, we will calculate the potential energy of the rock relative to the base of the cliff using the formula:
a. Potential energy = mass x gravity x height
Given:
Mass (m) = 20 kg
Gravity (g) = 9.8 m/s^2
Height (h) = 100 m
Potential energy = 20 kg x 9.8 m/s^2 x 100 m
Potential energy = 19,600 J
b. To find the kinetic energy just before the rock strikes the ground, we can use the conservation of energy principle. Since the rock falls freely, all the potential energy will be converted to kinetic energy.
Kinetic energy = Potential energy
Kinetic energy = 19,600 J
c. To find the speed of the rock as it strikes the ground, we can use the formula:
Kinetic energy = 0.5 x mass x speed^2
Given:
Mass (m) = 20 kg
Kinetic energy = 19,600 J
19,600 J = 0.5 x 20 kg x speed^2
speed^2 = 19,600 J / (0.5 x 20 kg)
speed^2 = 19,600 J / 10 kg
speed^2 = 1960 m^2/s^2
Taking the square root on both sides:
speed = √(1960 m^2/s^2)
speed ≈ 44.27 m/s
Therefore, the speed of the rock as it strikes the ground is approximately 44.27 m/s.
2) To calculate the work done by Justin in moving his girlfriend, we can use the formula:
Work = force x distance
Given:
Force (F) = 79 N
Distance (d) = 120 m
a. Work = 79 N x 120 m
Work = 9480 J
Therefore, Justin did 9480 Joules of work in moving his girlfriend.
b. To calculate the power expended by Justin, we can use the formula:
Power = work / time
Given:
Work (W) = 9480 J
Time (t) = 4 minutes = 240 seconds
b. Power = 9480 J / 240 s
Power = 39.5 W
Therefore, Justin expended 39.5 Watts of power to move this distance.
1) a. The potential energy possessed by the rock can be calculated using the formula: Potential Energy = mass x acceleration due to gravity x height. The mass of the rock is 20 kg, the acceleration due to gravity is approximately 9.8 m/s^2, and the height of the cliff is 100 m. Plugging these values into the formula, we get:
Potential Energy = (20 kg) x (9.8 m/s^2) x (100 m) = 19600 Joules.
b. When the rock falls, its potential energy gets converted into kinetic energy. The formula for kinetic energy is: Kinetic Energy = 0.5 x mass x velocity^2. Since the mass of the rock is 20 kg, we need to find its velocity just before it strikes the ground.
c. To calculate the velocity of the rock just before it strikes the ground, we can use the equation of motion: v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration (in this case, acceleration due to gravity), and s is the distance. In this scenario, the initial velocity of the rock is 0 (as it starts from rest), the acceleration is 9.8 m/s^2, and the distance is the height of the cliff, which is 100 m. Plugging in these values, we can solve for v:
v^2 = 0 + 2(9.8 m/s^2)(100 m)
v^2 = 1960 m^2/s^2
v ≈ 44.27 m/s (rounded to two decimal places)
Therefore, just before it strikes the ground, the rock has a speed of approximately 44.27 m/s.
2) a. The work done by Justin can be calculated using the formula: Work = force x distance. Justin pulls his girlfriend with a constant force of 79 N over a distance of 120 m. Plugging in these values, we get:
Work = (79 N) x (120 m) = 9480 Joules.
b. Power is defined as the rate at which work is done. It can be calculated using the formula: Power = Work / time. In this case, the work done is 9480 Joules, and the time taken is 4 minutes, which is equivalent to 240 seconds.
Therefore, the power expended by Justin is:
Power = (9480 Joules) / (240 seconds) = 39.5 Watts.
Number two is way off the mark.
work=force*distance=79*120 joules