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A crate of mass 86 kg is accelerating down a surface inclined at an angle of 25° to the horizontal - NSC Physical Sciences - Question 3 - 2016 - Paper 1
Question 3
A crate of mass 86 kg is accelerating down a surface inclined at an angle of 25° to the horizontal. A man applies a force F upwards parallel to the plane in an atte... show full transcript
Worked Solution & Example Answer:A crate of mass 86 kg is accelerating down a surface inclined at an angle of 25° to the horizontal - NSC Physical Sciences - Question 3 - 2016 - Paper 1
Step 1
3.1 The applied force F is a non-conservative force. What is meant by a non-conservative force?
Answer
A non-conservative force is a type of force for which the work done is path-dependent, meaning that the work done by this force in moving an object between two points depends on the route taken. Non-conservative forces, such as friction, do not store energy in a potential form, and thus, the work done against these forces is not recoverable. In contrast, conservative forces, like gravitational force, store energy in a potential form, allowing the energy to be fully recovered.
Step 2
3.2 The coefficient of kinetic friction (μk) between the crate and the surface of the plane is 0,22. Prove that the magnitude of the kinetic frictional force is 168,04 N.
Answer
To find the kinetic frictional force, we can use the formula:
Where:
- (coefficient of kinetic friction)
- is the normal force which can be calculated as given the gravitational force acting on the crate, adjusted for the incline:
Given:
- Mass
- Gravitational acceleration
- Angle
Calculating the normal force:
ightarrow 86 imes 8.88 = 764.08 ext{ N}$$ Now, substituting into the kinetic friction formula: $$F_k = 0.22 imes 764.08 = 168.04 ext{ N}$$Step 3
3.3 State work-energy theorem in words.
Answer
The work-energy theorem states that the work done by the net force acting on an object is equal to the change in the object's kinetic energy. This means that if a net force does work on an object, it causes a change in the speed of the object, resulting in a change in kinetic energy.
Step 4
3.4 Draw a labelled free-body diagram of all the forces acting on the crate.
Answer
The free-body diagram will include:
- The weight force () acting downward, equal to , where .
- The normal force () acting perpendicular to the surface.
- The frictional force () acting against the direction of motion, calculated previously.
- The applied force () acting parallel to the surface, attempting to oppose the weight component along the incline.
Step 5
3.5 The crate accelerates parallel down the inclined plane for a distance of 0,9 m at 1,54 m·s². Use the work-energy theorem and calculate the work done on the crate.
Answer
According to the work-energy theorem:
First, calculate the initial kinetic energy with the formula: K.E_{ ext{initial}} = rac{1}{2}mv_i^2 Assuming (the crate starts from rest):
K.E_{ ext{initial}} = rac{1}{2} imes 86 imes 0^2 = 0
Now calculate the final kinetic energy after accelerating: K.E_{ ext{final}} = rac{1}{2}mv_f^2 Using the kinematic equation to find :
ightarrow v_f = ext{sqrt}(2.772) ≈ 1.67 ext{ m/s}$$ Now substituting into the kinetic energy formula: $$K.E_{ ext{final}} = rac{1}{2} imes 86 imes (1.67)^2 = rac{1}{2} imes 86 imes 2.7889 ≈ 119.03 ext{ J}$$ Thus, the work done on the crate is: $$W = K.E_{ ext{final}} - K.E_{ ext{initial}} = 119.03 - 0 = 119.03 ext{ J}$$