A block of mass 2.40 kg is pushed 2.09 m along a frictionless horizontal table by a constant 18.6 N force directed 23.7o below the horizontal. Determine the work done by the applied force.
Determine the magnitude of the normal force exerted by the table.
Determine the magnitude of the force of gravity
Determine the net force on the block.
(a) the work done by the applied force
W=F(x) •s=F•cos α•s= 18.6•cos23.7•2.09 = ….
(b) the magnitude of the normal force exerted by the table
N =mg+F(y) =mg+Fsin α = 2.4•9.8 +18.6•sin23.7 = …
(c) the magnitude of the force of gravity
mg = 2.4•9.8 = …
(d) F(net) =F(x) = F•cos α•= 48.6•cos23.7= …
To determine the work done by the applied force, you can use the equation:
Work = Force * Distance * cos(theta),
where Force is the applied force, Distance is the distance the block is pushed, and theta is the angle between the direction of force and displacement. Plugging in the values given:
Force = 18.6 N,
Distance = 2.09 m,
theta = 23.7o,
Work = 18.6 N * 2.09 m * cos(23.7o).
To calculate the cosine of 23.7o, you can use a calculator or trigonometric tables. Let's assume the cosine value is approximately 0.920. Plugging it into the equation:
Work = 18.6 N * 2.09 m * 0.920.
Now, you can calculate the work done by multiplying the values:
Work = 38.41 J.
Therefore, the work done by the applied force is 38.41 Joules.
To determine the magnitude of the normal force exerted by the table, you can use the fact that the normal force is equal in magnitude and opposite in direction to the force of gravity when an object is on a horizontal surface with no vertical acceleration. In this case, the force of gravity is given by:
Force of Gravity = mass * acceleration due to gravity.
Given the mass of the block is 2.40 kg and the acceleration due to gravity is approximately 9.8 m/s^2, you can calculate the force of gravity:
Force of Gravity = 2.40 kg * 9.8 m/s^2.
Calculating:
Force of Gravity = 23.52 N.
Therefore, the magnitude of the normal force exerted by the table is 23.52 Newtons.
To determine the net force on the block, you can use 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:
Net Force = mass * acceleration.
Since the block is moving along the frictionless table with a constant velocity, its acceleration is zero. Therefore, the net force on the block is also zero.
Therefore, the net force on the block is 0 Newtons.