A tow truck does 3.5 k j of pulling horizontally on a stalled truck to move 2.8 m horizontally in the direction of the force. What is the magnitude of the force.
To find the magnitude of the force, we can use the work-energy principle. The work done by the tow truck is equal to the change in kinetic energy of the stalled truck.
The work done by the tow truck is given as 3.5 kJ (kilojoules).
The change in kinetic energy of the stalled truck can be calculated using the formula:
ΔK = (1/2)mv^2
Where ΔK is the change in kinetic energy, m is the mass of the truck, and v is the velocity.
Since the truck is stalled, it initially has no velocity, so the initial kinetic energy (K1) is zero.
ΔK = K2 - K1 = K2 - 0 = K2
Therefore, the work done by the tow truck is equal to the change in kinetic energy, which can be expressed as:
3.5 kJ = ΔK
Now, we need to calculate the final kinetic energy (K2) of the stalled truck. We can use the formula for work:
Work (W) = Force (F) * Distance (d) * cos(θ)
Where θ is the angle between the direction of force and the direction of motion.
Since the force and motion are in the same direction, θ = 0, and cos(0) = 1.
So, we have:
3.5 kJ = F * 2.8 m * cos(0)
cos(0) = 1
3.5 kJ = F * 2.8 m
To find the force (F), we rearrange the equation:
F = (3.5 kJ) / (2.8 m)
Now, let's convert kilojoules (kJ) to joules (J) for consistency:
1 kJ = 1000 J
F = (3.5 kJ * 1000 J/kJ) / 2.8 m
F = 3500 J / 2.8 m
F ≈ 1250 N
Therefore, the magnitude of the force exerted by the tow truck is approximately 1250 Newtons.