Final answer:
The mass of the ball of putty that, when dropped onto a moving cart, caused its speed to reduce from 1.70 m/s to 1.53 m/s is calculated to be 0.167 kg (or 167 grams) by applying the conservation of momentum formula for an inelastic collision.
Step-by-step explanation:
To calculate the mass of the ball of putty dropped onto a cart causing a reduction in speed, we can apply the conservation of momentum, which states that the total momentum before a collision is equal to the total momentum after the collision, assuming no external forces act on the system.
The formula for conservation of momentum in a completely inelastic collision, where the two objects stick together after the collision, is given by:
m1 × v1 before + m2 × v2 before = (m1 + m2) × v after
We know the following:
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- Mass of cart, m1 = 1.50 kg
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- Initial speed of the cart, v1 before = 1.70 m/s
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- Final speed of the cart and putty, v after = 1.53 m/s
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- Initial speed of the putty, v2 before = 0 m/s (as it is dropped from a stationary hand)
Substitute these values into the momentum conservation formula:
1.50 kg × 1.70 m/s + m2 × 0 m/s = (1.50 kg + m2) × 1.53 m/s
Simplify and solve for m2 (mass of the putty):
m2 = ((1.50 kg × 1.70 m/s) - (1.50 kg × 1.53 m/s)) / (1.53 m/s)
Calculate the mass of the putty:
m2 = (2.55 kg·m/s - 2.295 kg·m/s) / 1.53 m/s
m2 = 0.167 kg or 167 grams