Question

A picture of a person pulling a sled by a rope at an angle. A child is sitting on the sled.
A free body diagram with 5 force vectors. The first vector is pointing downward, labeled F Subscript g Baseline = 58.8 N. The second vector is pointing right, labeled F Subscript f Baseline = 1.5 N. The third vector is pointing upward. The fourth vector is pointing left, labeled F Subscript p x Baseline. The fifth vector is pointing up to the left at an angle of 30 degrees, labeled F Subscript p Baseline = 10 N. The upward vector is shorter than the downward vector. The right vector is shorter than the left vector. Another vector starts at the tip of the left vector and points up to the tip of the 30 degree vector using the tip to tail method.
The force diagram represents a girl pulling a sled with a mass of 6.0 kg to the left with a force of 10.0 N at a 30.0 degree angle. There is a 1.5 N force of friction to the right. The force of gravity is 58.8 N.

What is the normal force acting on the sled? Round the answer to the nearest whole number.

N

What is acceleration of the sled? Round the answer to the nearest tenth.

m/s2

Answer 1

Calculate vertical and horizontal components of the pull:
- F_y = 10.0·sin30° = 10.0·0.5 = 5.0 N (up)
- F_x = 10.0·cos30° = 10.0·0.8660 = 8.66 N (left)

Normal force (no vertical acceleration):
N + F_y − mg = 0 → N = mg − F_y = 58.8 − 5.0 = 53.8 N → 54 N

Horizontal acceleration (left positive):
F_net = F_x − f = 8.66 − 1.5 = 7.16 N
a = F_net / m = 7.16 / 6.0 = 1.193... m/s^2 → 1.2 m/s^2 (to the left)

Answers:
- Normal force = 54 N
- Acceleration = 1.2 m/s^2 (to the left)