Question

A child pulls on a 90 N wagon with a force of 100 N at 37^o
above the horizontal. Calculate the acceleration of the wagon. Assume
that friction is negligible.
(a)8.7m/s^2
(b)9.6m/s^2
(c)3.4m/s^2
(d)7.1m/s^2

Answer 1

Answer on Question #51821, Physics, Mechanics | Kinematics | Dynamics

A child pulls on a $90\mathrm{N}$ wagon with a force of $100\mathrm{N}$ at $37{}^{\circ}$ above the horizontal. Calculate the acceleration of the wagon. Assume that friction is negligible.

(a) $8.7\mathrm{m} / \mathrm{s}^{2}$

(b) $9.6\mathrm{m} / \mathrm{s}^{2}$

(c) $3.4\mathrm{m} / \mathrm{s}^{2}$

(d) $7.1\mathrm{m} / \mathrm{s}^{2}$

Solution:

The force along $x$ axis is

$$F _ {x} = F \cos \theta = 1 0 0 * \cos 3 7 {}^ {\circ} = 7 9. 8 6 \mathrm {N}$$

The magnitude of force is equated to the product of the mass times the acceleration

$$F _ {x} = m a$$

The mass is

$$m = \frac {P}{g} = \frac {9 0}{9 . 8 1} = 9. 1 7 \mathrm {k g}$$

Thus,

$$a = \frac {F _ {x}}{m} = \frac {7 9 . 8 6}{9 . 1 7} = 8. 7 \mathrm {m / s ^ {2}}$$

Answer: (a) $8.7\mathrm{m} / \mathrm{s}^{2}$

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