Question

zanele has a mass of 40kg and is sitting inside a 20kg cart .zanele's friends pull a cart with a force of 500N at an angle of 20°to the horizontal ,using a light rope .the cart experiences a frictional force of 300N .calculate the net horizontal force acting on the cart calculate the change in the carts momentum if zanele's friends apply the force for 10s calculate the net horizontal force acting on zanele how would the cart's final velocity be affected if angle between the 500N force and the horizontal is decreased ?explain your answer.​

Answer 1

The net horizontal force acting on the cart is 169.85 N.

The change in the carts momentum is 5,000 Ns.

The net horizontal force on Zanele is same as the net horizontal force on the cart.

If angle between the 500N force and the horizontal is decreased, the final velocity of the cart increases.

The given parameters:

• Mass of zanele, m1 = 40 kg
• Mass of the cart, m2 = 20 kg
• Applied force, F = 500 N, at angle 20 degrees
• Frictional force on the cart, Ff = 300 N
• Time, t = 10 s

Net horizontal force on the cart;

• The net horizontal force acting on the cart is calculated as follows;

$F_{net} = F - F_f\\\\F_{net} = 500 \times cos(20) - 300\\\\F_{net} = 169.85 \ N$

Change in momentum;

• The change in the carts momentum at the given time of applied force is calculated as follows;

$\Delta mv = Ft \\\\\Delta mv = 500 \times 10= 5,000 \ Ns$

The net horizontal force on Zanele is same as the net horizontal force on the cart.

The final velocity of the cart;

• When the angle decreases the cart's final velocity would be affected  as follows;

$F_{net} = F - F_f\\\\F_{net} = \frac{mv}{t} \\\\\frac{mv}{t} = F - F_f\\\\ \frac{mv}{t} = Fcos(\theta) - F_f\\\\let \ \theta = 0^0\\\\\frac{mv}{t} =500 \times cos(0) - 300\\\\\frac{mv}{t} = 200\\\\v = \frac{200 t}{m} \\\\when \ \theta = 20^0\\\\\frac{mv}{t} =500 \times cos(20) - 300\\\\\frac{mv}{t} = 169.85\\\\v = \frac{169.85t}{m}$

Thus, if angle between the 500N force and the horizontal is decreased, the final velocity of the cart increases.

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