a string exerts a tension force of 55 N on a 10 kg block as it moves a distance of 5 up a frictionless incline, included at 37 degrees. the string pulls parallel to the incline.
find the gravitational PE on the system as the block moves 5 m up the incline and find the change inKE for the system as the block moves 5 m up the incline
To find the gravitational potential energy (PE) of the system as the block moves up the incline, we can use the formula:
PE = m * g * h
where m is the mass of the block, g is the acceleration due to gravity, and h is the height the block is lifted.
Given:
m = 10 kg (mass of the block)
h = 5 m (height the block is lifted)
The acceleration due to gravity, g, is approximately 9.8 m/s^2.
Substituting the values into the formula, we get:
PE = 10 kg * 9.8 m/s^2 * 5 m
PE = 490 J
Therefore, the gravitational potential energy on the system as the block moves 5 m up the incline is 490 Joules.
Now, let's calculate the change in kinetic energy (ΔKE) for the system as the block moves up the incline. The change in kinetic energy is given by the equation:
ΔKE = KE_final - KE_initial
Since the block starts from rest, its initial kinetic energy (KE_initial) is zero. We need to find the final kinetic energy (KE_final).
To calculate the final kinetic energy, we first need to determine the final velocity of the block after moving up the incline.
Since the incline is frictionless, the work done by the tension force is equal to the change in kinetic energy. The work done (W) is given by:
W = F * d * cosθ
Where F is the tension force exerted by the string, d is the distance moved along the incline, and θ is the angle between the force and the direction of motion (in this case, the angle of inclination, 37 degrees).
Given:
F = 55 N (tension force exerted by the string)
d = 5 m (distance moved along the incline)
θ = 37 degrees
Substituting the values, we have:
W = 55 N * 5 m * cos(37 degrees)
Now, since the work done (W) is equal to the change in kinetic energy (ΔKE), we can write:
ΔKE = W
Therefore, the change in kinetic energy for the system as the block moves 5 m up the incline is the value we obtained for W:
ΔKE = 55 N * 5 m * cos(37 degrees)