Question

Part IV Objects on an incline w/ Tension + Friction
1. A small 63 kg sleigh is pulled by a rein attached to horse up a 15'angle hill to the
horizontal. The tension of the rein is 510 N. The coefficient of kinetic friction is
0.25
a. What is the normal force that the sleigh exerts on the hill?
b. What are the magnitude and direction of the sleigh's acceleration?

Answer 1

(a) The normal force on the sleigh is 596.36 N.

(b) The magnitude and direction of acceleration of the sleigh is 3.2 m/s² upwards.

The given parameters;

• mass of the sleigh, m = 63 kg
• inclination of the hill, θ = 15⁰
• tension on the rein, F = 510 N
• coefficient of friction, μ = 0.25

The normal force on the sleigh is calculated as follows;

$F_n = mg \times cos(\theta)\\\\F_n = 63 \times 9.8 \times cos(15)\\\\F_n = 596.36 \ N$

The magnitude and direction of acceleration of the sleigh is calculated as follows;

$\Sigma F= ma\\\\F - mgsin(\theta) - F_f = ma\\\\F - mgsin(\theta) - \mu F_n = ma\\\\510\ - \ 63 \times 9.8 \times sin15 \ -\ 0.25\times 596.36 = 63a\\\\201 .11 = 63a\\\\a = \frac{201.11}{63} \\\\a = 3.2 \ m/s^2 \ upwards$

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