A truck with a heavy load has a total mass of 7100 kg. It is climbing a 15∘ incline at a steady 15 m/s when, unfortunately, the poorly secured load falls off! Immediately after losing the load, the truck begins to accelerate at 1.5 m/s2. Part A What was the mass of the load? Ignore rolling friction.

The load has a mass of 2636.8 kg

Explanation:

Step 1 : Data given

Mass of the truck = 7100 kg

Angle = 15°

velocity = 15m/s

Acceleration = 1.5 m/s²

Mass of truck = m1 kg

Mass of load = m2 kg

Thrust from engine = T

Step 2:

⇒ Before the load falls off, thrust (T) balances the component of total weight downhill:

T = (m1+m2) * g*sinθ

⇒ After the load falls off, thrust (T) remains the same but downhill component of weight becomes m1*gsinθ.

Resultant force on truck is F = T - m1*gsinθ

F causes the acceleration of the truck: F = m*a

This gives the equation:

T - m1*gsinθ = m1*a

T = m1 (a + gsinθ)

Combining both equations gives:

(m1+m2) * g*sinθ = m1 * (a + gsinθ)

m1*g*sinθ + m2*g*sinθ = m1*a + m1*g*sinθ

m2*g*sinθ = m1*a

Since m1+m2 = 7100kg, m1 = 7100 - m2. This we can plug into the previous equation:

m2*g*sinθ = (7100 - m2) * a

m2*g*sinθ = 7100a - m2a

m2*gsinθ + m2*a = 7100a

m2 * (gsinθ + a) = 7100a

m2 = 7100a / (gsinθ + a)

m2 = (7100 * 1.5) / (9.8sin (15°) + 1.5)

m2 = 2636.8 kg

The load has a mass of 2636.8 kg