An 85.7 N box of clothes is pulled 26.2 m up
a 31.7
◦
ramp by a force of 112 N that points
along the ramp.
The acceleration of gravity is 9.81 m/s
2
.
If the coefficient of kinetic friction between
the box and ramp is 0.24, calculate the change
in the box’s kinetic energy.
Answer in units of J
ΔKE=ΔPE +W(fr)= m•g•s•sinα+μ•m•g•s•cosα=
=m•g•s(sinα+μ•cosα)
To calculate the change in the box's kinetic energy, we need to first find the work done on the box. The work done is equal to the force applied multiplied by the distance moved in the direction of the force:
Work = Force × Distance
In this case, the force applied is the component of the force parallel to the direction of motion, which is given as 112 N. The distance moved in the direction of the force is the vertical distance traveled by the box, which is 26.2 m.
Work = 112 N × 26.2 m
Next, we need to calculate the work done against friction. The force of friction is calculated as the product of the coefficient of kinetic friction (0.24) and the normal force. The normal force is the force perpendicular to the ramp's surface, which is equal to the weight of the box. The weight of the box can be calculated as the mass of the box multiplied by the acceleration due to gravity (9.81 m/s^2).
Weight of the box = mass × acceleration due to gravity
= 85.7 N / 9.81 m/s^2
Force of friction = coefficient of kinetic friction × normal force
= 0.24 × (85.7 N / 9.81 m/s^2)
Now, we can calculate the work done against friction by multiplying the force of friction by the distance moved, which is 26.2 m.
Work against friction = Force of friction × Distance
= (0.24 × (85.7 N / 9.81 m/s^2)) × 26.2 m
Finally, we can calculate the change in kinetic energy by subtracting the work done against friction from the total work done:
Change in kinetic energy = Total work - Work against friction
Substituting the values we have:
Change in kinetic energy = (112 N × 26.2 m) - ((0.24 × (85.7 N / 9.81 m/s^2)) × 26.2 m)
Calculate the expression to find the change in kinetic energy. The resulting value will be in units of Joules (J).