A force of 50 N directed at an angle of 45 degrees from the horizontal pulls a 70 kg sled across a frictionless pond. The acceleration of the sled is most nearly (sin 45 degrees = cos 45 degrees = 0.7).
50 cos 45 = 35
f = m a
35 = 70 a
a = 35/70 = .5 m/s^2
To find the acceleration of the sled, we can use Newton's second law of motion, which states that the acceleration of an object is equal to the net force acting on it divided by its mass.
Given:
Force (F) = 50 N
Angle (θ) = 45 degrees
Mass (m) = 70 kg
First, determine the horizontal component of the force:
F_horizontal = F * cos(θ) = 50 N * 0.7 ≈ 35 N
Next, use Newton's second law to find the acceleration:
acceleration (a) = F_horizontal / m = 35 N / 70 kg = 0.5 m/s²
Therefore, the acceleration of the sled is approximately 0.5 m/s².
To determine the acceleration of the sled, we can apply Newton's second law, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
In this case, the force pulling the sled is 50 N, and it is directed at an angle of 45 degrees from the horizontal. To find the horizontal component of this force, we need to multiply it by the cosine of the angle (cos 45 degrees = 0.7). Therefore, the horizontal component of the force is 50 N * 0.7 = 35 N.
Since there is no friction on the pond, the only force acting on the sled is the horizontal component of the pulling force. Therefore, we can equate this force to the mass of the sled multiplied by its acceleration:
35 N = 70 kg * acceleration
To find the acceleration, we can now rearrange the equation:
acceleration = 35 N / 70 kg
Simplifying, we get:
acceleration = 0.5 m/s^2
Therefore, the acceleration of the sled is approximately 0.5 m/s^2.