1. A 12 kg wagon is being pulled at an angle of 38o above horizontal. What force is applied to
the wagon if it accelerates from rest to a speed of 2.2 m/s over a distance of 3.4 m? (4 marks)
2. A 31.0 kg child on a swing reaches a maximum height of 1.92 m above their rest position.
Assuming no loss of energy: (8 marks)
a) At what point during the swing will she attain their maximum speed?
b) What will be her maximum speed through the subsequent swing?
c) Assuming this maximum height was the result of one push from her parent, what was the
average force exerted by the parent if they pushed over a distance of 152 cm?
3. A 75.0 kg novice skier is going down a hill with several secondary hills. Ignore frictional effects
and assume the skier does not push off or slow himself down. If the initial hill is 38.7 m above the
chalet level: (8 marks)
a) What is the speed of the skier at the bottom of the first hill, 25.6 m above the chalet level?
b) At what height does the skier have a speed of 12.0 m/s?
c) What is the skier's speed at the bottom of the hill?
d) Is this a realistic scenario?
It would appear as homework dumping if you don't show your work.
Also, if you make an effort to solve the first one, there is a chance you can apply what you learned to solve the other ones, or at least get a good kick-start.
I suggest you review class material, attempt the first question, and then post where you have a problem.
Some useful formulas:
Horizontal component of force P
=P(cos(θ))
v^2-u^2=2aS
S=distance
u,v=initial/final velocities
a=acceleration
Kinetic energy=potential energy:
(1/2)mv^2 = mgh
To solve these physics problems, you can use the principles of Newton's laws of motion, specifically the equations related to force, acceleration, and energy. Here's a step-by-step explanation of how to solve each problem:
1. For the first problem, you need to use Newton's second law of motion, which states that the net force applied to an object is equal to the product of its mass and acceleration. In this case, the force is being applied at an angle, so you'll need to break it down into its horizontal and vertical components. The horizontal component doesn't contribute to the acceleration since it's perpendicular to the direction of motion, so you only need to consider the vertical component.
a) The force applied to the wagon can be found using the formula: F = m * a, where m is the mass of the wagon and a is the acceleration. In this case, the acceleration can be found using the equation of motion: v² = u² + 2as, where v is the final velocity (2.2 m/s), u is the initial velocity (0 m/s), a is the acceleration, and s is the distance (3.4 m). Rearranging the equation, you can solve for a: a = (v² - u²) / (2s). Plug in the given values and solve for a.
b) To find the vertical component of the force, you can use the equation: F = m * g * sin(θ), where m is the mass of the wagon, g is the acceleration due to gravity (9.8 m/s²), and θ is the angle of the force (38°). Plug in the values and solve for F.
2. This problem involves the concept of energy conservation in a swinging motion. The maximum height reached by the child is the potential energy at its peak, which is converted into kinetic energy at the maximum speed. The total mechanical energy remains constant throughout the swing.
a) To find the point during the swing where the child attains maximum speed, you need to determine the point where all potential energy is converted into kinetic energy. At the highest point, all potential energy is converted, so the child reaches maximum speed at the highest point of the swing.
b) To find the maximum speed in subsequent swings, you can use the principle of conservation of mechanical energy. At the highest point of each subsequent swing, the potential energy is converted into kinetic energy, which can be calculated using the equation: KE = 0.5 * m * v^2, where m is the mass of the child (31.0 kg) and v is the maximum speed. Rearrange the equation, plug in the given values, and solve for v.
c) Assuming the maximum height was the result of one push from the parent, you can calculate the average force exerted by the parent using the work-energy principle: Work = Force * Distance. The work is equal to the change in potential energy, which is given by m * g * h, where m is the mass of the child, g is the acceleration due to gravity (9.8 m/s²), and h is the maximum height above the rest position. Rearrange the equation, plug in the given values, and solve for the average force (F).
3. This problem involves analyzing the motion of a skier going downhill. Ignoring frictional effects and assuming no external forces are acting on the skier, you can analyze the change in potential energy and the conservation of mechanical energy.
a) To find the speed of the skier at the bottom of the first hill, you can use the principle of conservation of mechanical energy. The initial potential energy at the top of the hill is given by m * g * h1, where m is the mass of the skier (75.0 kg), g is the acceleration due to gravity (9.8 m/s²), and h1 is the height of the initial hill. The final kinetic energy at the bottom of the hill is given by 0.5 * m * v^2, where v is the speed at the bottom of the hill. Equate the two energies and solve for v.
b) The height at which the skier has a speed of 12.0 m/s can be calculated using the principle of conservation of mechanical energy. The initial potential energy at the top of the hill is given by m * g * h1, where h1 is the initial height. The final kinetic energy at the desired speed is given by 0.5 * m * v^2, where v is the desired speed (12.0 m/s). Equate the two energies and solve for h.
c) To find the skier's speed at the bottom of the hill, you can use the principle of conservation of mechanical energy. The initial potential energy at the top of the hill is given by m * g * h2, where h2 is the height of the hill. The final kinetic energy at the bottom of the hill is given by 0.5 * m * v^2, where v is the speed at the bottom of the hill. Equate the two energies and solve for v.
d) Lastly, you need to determine if this scenario is realistic. Realistically, there would be frictional forces acting on the skier, which would cause some energy to be converted into heat. Additionally, the skier would encounter air resistance. By ignoring these factors, the scenario described is an idealized situation that doesn't take into account real-world effects.