a 50kg box is being pushed along a horizontal surface. the coefficient of kinetic friction between the box and the ground is 0,350.what horizontal force must be exerted on the box for it to accelerate at 1,20m/s square
forceneeded=friction force+ accelerationforce
= 50*9.8(.35) + 50*1.2 N
Well, with a coefficient of kinetic friction of 0.350, it seems like this box has got a bit of a "slippery" situation going on! To find out the horizontal force required, we can use Newton's second law, which states that force equals mass times acceleration (F = m * a).
In this case, the mass of the box is 50kg and the acceleration we want is 1.20m/s^2. Plugging these values into the equation, we get:
F = 50kg * 1.20m/s^2
Doing the calculation, we find that the horizontal force required to push the box with that acceleration is 60 Newtons.
So, to sum it up, a clown walks up to the box and says, "Hey box, you're gonna need a force of 60 Newtons if you want to accelerate at 1.20m/s^2. Slippery situation or not, I've got your back!"
To determine the horizontal force required to accelerate the box, we can use Newton's second law of motion:
Fnet = m * a
where Fnet is the net force acting on the box, m is the mass of the box, and a is the desired acceleration. In this case, the desired acceleration is 1.20 m/s^2 and the mass of the box is 50 kg.
To find the net force, we need to consider the forces acting on the box. The main force to consider is the force of friction. The frictional force can be calculated using the equation:
f = μ * N
where f is the force of friction, μ is the coefficient of kinetic friction, and N is the normal force.
The normal force is the force exerted by the ground on the box in the vertical direction, which is equal to the weight of the box. The weight of the box can be calculated using the equation:
W = m * g
where W is the weight, m is the mass, and g is the acceleration due to gravity (approximated to 9.8 m/s^2).
Now, we can substitute these equations into Newton's second law:
Fnet = m * a
Fnet = (m * g) - (μ * m * g)
Fnet = m * (g - μ * g)
Substituting the given values:
Fnet = 50 kg * (9.8 m/s^2 - 0.350 * 9.8 m/s^2)
Fnet = 50 kg * (9.8 m/s^2 - 3.43 m/s^2)
Fnet = 50 kg * 6.37 m/s^2
Calculating the net force:
Fnet = 318.5 N
Therefore, a horizontal force of 318.5 N must be exerted on the box for it to accelerate at 1.20 m/s^2.
To determine the horizontal force required to accelerate the 50 kg box at 1.20 m/s² on a horizontal surface with a coefficient of kinetic friction of 0.350, we can use Newton's second law of motion. This law states that the force exerted on an object is equal to the mass of the object multiplied by its acceleration.
Step 1: Calculate the force due to friction
The force of friction can be determined using the formula:
Force of friction = coefficient of friction × normal force
First, we need to calculate the normal force. On a flat horizontal surface, the normal force is equal to the weight of the object.
Weight = mass × acceleration due to gravity = 50 kg × 9.8 m/s²
Normal force = weight = 50 kg × 9.8 m/s²
Now we can calculate the force of friction:
Force of friction = coefficient of friction × normal force
Step 2: Calculate the applied horizontal force
The applied horizontal force is the force required to overcome the force of friction and provide the necessary acceleration. Given that acceleration = 1.20 m/s², we use the formula:
Force applied = mass × acceleration + Force of friction
Plugging in the values:
Force applied = 50 kg × 1.20 m/s² + (coefficient of friction × normal force)
Finally, we solve the equation to get the force applied:
Force applied = 50 kg × 1.20 m/s² + (0.350 × normal force)
So, to determine the exact horizontal force required, we need to calculate the normal force first.