A force of 60N acts on a box with a mass of 35.0 kg sitting on the floor. The force acts at an angle of 30º with the horizontal, and the coefficient of kinetic friction between the surfaces is 0.15.
a) What is the normal force on the box exerted by the floor?
b) What is the magnitude of the resultant acceleration of the box?
force acts at an angle of 30º with the horizontal,
( Up or down ?
I’m not sure that’s all that is given
well, if pushing with component down
F down on floor = 60 sin 30 + 35 * 9.81 = 30 + 343 = 373 Newtons
( Use -30 if pulling up with rope)
friction force = 0.15 *373 = 55.95
60 cos 30 = 52 N
well, no acceleration, better pull instead of push
now F down = 313 N
friction force = 0.15* 313 = 47 N
52 -47 = 5 Newtons
F = m a
5= 35 a
a = 1/7 m/s^2 = 0.143
To find the answers to these questions, we can break down the given information and apply Newton's laws of motion. Let's go step by step:
a) To find the normal force on the box exerted by the floor, we need to consider that when an object rests on a horizontal surface, the normal force is equal in magnitude and opposite in direction to the weight of the object. The weight of an object can be calculated using the formula W = m * g, where W is the weight, m is the mass, and g is the acceleration due to gravity (which is approximately 9.8 m/s^2).
In this case, the mass of the box is given as 35.0 kg. Therefore, the weight of the box is W = 35.0 kg * 9.8 m/s^2.
Next, we need to consider the angle at which the force is acting on the box. Since the force is acting at an angle of 30º with the horizontal, we can find the horizontal component of the force by multiplying the magnitude of the force (60N) by the cosine of the angle (cos 30º). The formula for calculating the horizontal component is Fx = F * cosθ.
Now we can equate the normal force and the weight of the box, since they are equal in magnitude and opposite in direction. We can set up the equation:
Normal force = Weight of the box
Normal force = m * g
Finally, we can substitute the given values into the equation to find the normal force.
b) To find the magnitude of the resultant acceleration of the box, we'll use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by the acceleration of the object. The formula is F_net = m * a, where F_net is the net force, m is the mass, and a is the acceleration.
The net force acting on the box is the horizontal component of the force minus the force of friction. The force of friction can be found using the formula F_friction = μ * N, where μ is the coefficient of kinetic friction and N is the normal force.
We can substitute this equation into Newton's second law, rearrange it to solve for acceleration, and substitute the given values to find the magnitude of the resultant acceleration.
By following these steps, you should be able to find the answers to both questions.