A truck carrying a 38 kg crate accelerates uniformly from rest to 87.5 km/hr in 12.1 s. Calculate the work done on the crate by the truck.
Please help:/
km/h -> m/s
W=ΔKE=KE2-KE1=mv²/2- 0= mv²/2
To calculate the work done on the crate by the truck, we can use the work-energy principle. The work done is equal to the change in kinetic energy of the crate.
First, we need to calculate the initial and final kinetic energies of the crate.
The initial velocity of the crate is 0 m/s because it starts from rest.
To find the final velocity, we need to convert 87.5 km/hr to m/s. We know that 1 km/hr is equal to 0.2778 m/s.
So, the final velocity of the crate is 87.5 km/hr * 0.2778 m/s = 24.3 m/s.
Now, let's calculate the initial and final kinetic energies using the kinetic energy formula:
Kinetic energy = 0.5 * mass * velocity^2
The initial kinetic energy is:
K(initial) = 0.5 * 38 kg * (0 m/s)^2 = 0 J
The final kinetic energy is:
K(final) = 0.5 * 38 kg * (24.3 m/s)^2
K(final) = 0.5 * 38 kg * 590.49 m^2/s^2
K(final) = 11,207.43 J
Now we can calculate the work done:
Work = K(final) - K(initial)
Work = 11,207.43 J - 0 J
Work = 11,207.43 J
Therefore, the work done by the truck on the crate is 11,207.43 Joules.
To calculate the work done on the crate by the truck, we need to use the work-energy principle:
The work-energy principle states that the work done on an object is equal to the change in its kinetic energy.
First, let's convert the final velocity from km/hr to m/s:
87.5 km/hr = 87.5 * (1000 m/1 km) * (1 hr/3600 s) = 24.31 m/s
Next, we can calculate the change in kinetic energy (ΔKE) using the equation:
ΔKE = 0.5 * m * (vf^2 - vi^2)
where m is the mass of the crate and vf and vi are the final and initial velocities, respectively. Since the truck starts from rest, the initial velocity is 0 m/s.
ΔKE = 0.5 * 38 kg * (24.31 m/s)^2 - 0.5 * 38 kg * (0 m/s)^2
= 0.5 * 38 kg * (591.6161 m^2/s^2)
= 11198.6118 J (joules)
Therefore, the work done on the crate by the truck is 11198.6118 J.