A Box (15.0 kg) is pulled up a 37 degree ramp with a force of 295 N. The frictional force acting on the block is 56.0 N. If Box travels 12.0 m up the ramp, determine the change in Box’s PEgrav.
PE change= workin-frictionalloss
workin=pullingforce*distance
frictionalloss=frictionforce*distance
To determine the change in the box's gravitational potential energy (PEgrav), we need to calculate the initial and final PEgrav values and then find the difference between them.
The formula for calculating the gravitational potential energy is:
PEgrav = m * g * h
Where:
m is the mass of the object (in this case, the box) in kilograms,
g is the acceleration due to gravity (approximately 9.8 m/s² on Earth),
h is the height or vertical displacement in meters.
First, we need to find the initial and final heights of the box on the ramp.
Given:
Mass of the box (m) = 15.0 kg
Force applied (F) = 295 N
Frictional force (friction) = 56.0 N
Distance traveled (d) = 12.0 m
Angle of the ramp (θ) = 37 degrees
To find the initial height (h_initial), we need to calculate the vertical component of the force applied:
F_vertical = F * sin(θ)
h_initial = F_vertical / (m * g)
Now let's calculate:
F_vertical = 295 N * sin(37°) = 295 N * 0.6018 ≈ 177.36 N
h_initial = 177.36 N / (15.0 kg * 9.8 m/s²) ≈ 1.20 m
Next, we need to find the final height (h_final) using the distance traveled:
h_final = d * sin(θ)
h_final = 12.0 m * sin(37°) ≈ 7.20 m
Now we can calculate the initial and final PEgrav:
PEgrav_initial = m * g * h_initial
PEgrav_final = m * g * h_final
PEgrav_initial = 15.0 kg * 9.8 m/s² * 1.20 m ≈ 176.4 J
PEgrav_final = 15.0 kg * 9.8 m/s² * 7.20 m ≈ 1026.0 J
Finally, we can determine the change in PEgrav:
ΔPEgrav = PEgrav_final - PEgrav_initial
ΔPEgrav = 1026.0 J - 176.4 J ≈ 849.6 J
So, the change in the box's gravitational potential energy is approximately 849.6 Joules.