An object with a mass of 0.75 kg is projected over a horizontal surface with a speed of 2.5 m/s. It then comes to rest after 3.0 s.
(b) How much work is done on the object?
The work done on the object is equal to the change in kinetic energy of the object. The kinetic energy of the object is given by KE = 0.5mv2, where m is the mass of the object and v is its velocity.
The initial kinetic energy of the object is 0.5 x 0.75 kg x (2.5 m/s)2 = 3.44 J.
The final kinetic energy of the object is 0 J, since it comes to rest after 3.0 s.
Therefore, the work done on the object is equal to the change in kinetic energy, which is 3.44 J.
To calculate the work done on the object, we need to use the work-energy principle. The work done on an object is equal to the change in its kinetic energy.
The initial kinetic energy (KE) of the object can be calculated using the formula:
KE = 0.5 * mass * velocity^2
where mass = 0.75 kg and velocity = 2.5 m/s.
KE_initial = 0.5 * 0.75 kg * (2.5 m/s)^2
= 0.5 * 0.75 kg * 6.25 m^2/s^2
= 1.875 J
The final kinetic energy of the object is zero since it comes to rest.
Therefore, the work done on the object can be calculated as:
Work = KE_final - KE_initial
Work = 0 - 1.875 J
Work = -1.875 J
So, the work done on the object is -1.875 Joules.
To determine the amount of work done on the object, we need to use the work-energy principle. This principle states that the work done on an object is equal to the change in its kinetic energy.
The kinetic energy of an object is given by the formula: KE = (1/2)mv^2, where m is the mass of the object and v is its velocity.
In this case, we know the mass of the object is 0.75 kg and it is moving with an initial velocity of 2.5 m/s. We also know that the object comes to rest, which means its final velocity is 0 m/s.
First, let's calculate the initial kinetic energy:
KE_initial = (1/2) * m * v^2 = (1/2) * 0.75 kg * (2.5 m/s)^2 = 1.40625 Joules
Next, let's calculate the final kinetic energy since the object comes to rest:
KE_final = (1/2) * m * v^2 = (1/2) * 0.75 kg * (0 m/s)^2 = 0 Joules
The change in kinetic energy is: ΔKE = KE_final - KE_initial = 0 J - 1.40625 J = -1.40625 J
Since the object is coming to rest, the work done on it is equal to the negative change in kinetic energy: Work = -ΔKE = -(-1.40625 J) = 1.40625 J
Therefore, the amount of work done on the object is 1.40625 Joules.