Inclined Plane Problem Set
Follow the Problem Set Instructions & Rubric to complete and submit the following questions:
1. A 1975 kg car is parked at the top of a steep 42 m long hill inclined at an angle of \( 15^o \). If the car starts rolling down the hill, how fast will it be going when it reaches the bottom of the hill? (Neglect friction.) [Answer: 15 m/s down the ramp]
2. Starting from rest, a cyclist coasts down the starting ramp at a professional biking track. If the ramp has the minimum legal dimensions (1.5 m high and 12 m long), find:
a) the acceleration of the cyclist, ignoring friction [Answer: 1.2 m/s\( ^2 \)]
b) the acceleration of the cyclist if all sources of friction yield an effective coefficient of friction of 0.11 [Answer: 0.14 m/s\( ^2 \)]
c) the time taken to reach the bottom of the ramp if friction acts as in (b) [Answer: 13s]
3. A skier coasts down a \( 3.5^o \) slope at constant speed. Find the coefficient of kinetic friction between the skis and the snow covering the slope. [Answer: 0.061]
4. A 2.0 kg box is put on the surface of an inclined plane at \( 27^o \) with the horizontal. The surface of the inclined plane is assumed to be frictionless.
a) Draw a free body diagram of the box on the inclined plane and label all forces acting on the box.
b) Determine the acceleration of the box down the plane. [Answer: 4.5 \( m/s^2 \))
c) Determine the magnitude of the force exerted by the inclined plane on the box. [Answer: 17 N]
5. A particle of mass 5.0 kg rests on a \( 30^o \) inclined plane with the horizontal. A force \( F_a \) of magnitude \( 3.0 \times 10^1 N \) acts on the particle in the direction parallel and up the inclined plane.
a) Draw a free body diagram including the particle, the inclined plane and all forces acting on the particle with their labels.
b) Find the force of friction acting on the particle. [Answer: 5.5 N]
c) Find the normal force exerted by the inclined on the particle. [Answer: 42 N]
6. A \( 1.0 \times10^2 \) kg box is to be lowered at constant speed down an inclined plane 4.0 m long from the back of a lorry 2.0 m above the ground. The coefficient of kinetic friction is equal to 0.45. What is the magnitude of the force \( F_a \) to be applied parallel to the inclined plane to hold back the box so that it is lowered at constant speed? [Answer: 110 N]
7. A box of mass M = \( 1.0 \times10^1 \) kg rests on a \( 35^o \) inclined plane with the horizontal. A string is used to keep the box in equilibrium. The string makes an angle of \( 25^o \) with the inclined plane. The coefficient of friction between the box and the inclined plane is 0.30.
a) Draw a free body diagram including all forces acting on the particle with their labels.
b) Find the magnitude of tension T in the string. [Answer: 41 N]
c) Find the magnitude of the force of friction acting on the particle. [Answer: 19 N]
8. A box of mass M = 7.0 kg is held at rest on a \( 25^o \) inclined plane by force \( F_a \) acting horizontally as shown in the figure below. The box is on the point of sliding down the inclined plane. The static coefficient of friction between the box and the inclined plane is \( \mu_s =0.30 \). Find the magnitude of force \( F_a \). [Answer: 10 N]