A 400-kg object has a 100-Newton rightward net force being applied to it. What is the magnitude of the rightward acceleration on
1 answer:
Answer:
The answer to your question is a = 0.25 m/s²
Explanation:
Data
mass = m = 400 kg
Force = F = 100 N
acceleration = a = ? m/s²
Process
To solve this problem use Newton's second law that states that the force applied to an object is directly proportional to the mass of the body times its acceleration.
Formula
F = ma
solve for a
a =
Substitution
Simplification and result
a = 0.25 m/s²
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Answer:
Mass that one should put in the container so that the 100 g block slides down the inclined plane at constant speed = 34.16 g
Explanation:
The vertical forces (with respect to the inclined plane) acting on the 100 g block include the component of the weight of the block in the direction vertical to the inclined plane and the normal reaction of the plane on the block.
And sum of upward forces = sum of downward forces.
N = mg cos θ
m = 100 g = 0.10 kg
g = acceleration due to gravity = 9.8 m/s²
θ = 15°
N = (0.1×9.8×cos 15°) = 0.946582 N
The horizontal forces (With respect to the inclined plane) include the frictional force (acting upwards for the inclined plane, opposite to the intended direction of motion), the Tension in the rope (acting downwards, away from the 100 g block) and the horizontal component (with respect to the inclined plane) of the weight of the block, F, (also acting downards).
For the body to slide down the inclined plane at constant speed, the downward sloping forces must balance the frictional force, that is, there will be no acceleration.
Frictional force = Tension + F
Frictional force = μN
where μ = coefficient of kinetic friction = 0.60
N = normal reaction = 0.9466 N
Frictional force = Fr = (0.60 × 0.9466) = 0.56796 N = 0.568 N
The horizontal component (with respect to the inclined plane) of the weight of the block (also acting downards) = mg sin θ
F = (0.10 × 9.8 × sin 15°) = 0.253624 N
Tension in the rope = T = ?
Fr = F + T
T = Fr - F = 0.568 - 0.253624 = 0.314376 N = 0.3144 N
But the balance on the rope now has the total weight on the container (weight of container + weight on the container) to be equal to 2T.
2T = mg
2 × 0.3144 = 9.8m
m = 0.06416 kg = 64.16 g.
Mass of the container = 30 g
So, mass that one should put in the container so that the 100 g block slides down the inclined plane at constant speed = 64.16 - 30 = 34.16 g
Hope this Helps!!!
Answer:
(i) 7.2 feet per minute.
(ii) No, the rate would be different.
(iii) The rate would be always positive.
(iv) the resultant change would be constant.
(v) 0 feet per min
Explanation:
Let the length of ladder is l, x be the height of the top of the ladder from the ground and y be the length of the bottom of the ladder from the wall,
By making the diagram of this situation,
Applying Pythagoras theorem,
Differentiating with respect to t ( time ),
( l = 26 feet = constant )
We have,
(i) From equation (1),
From equation (X),
(ii) From equation (X),
Thus, for different value of x the value of would be different.
(iii) Since, distance = Positive number,
So, the value of y will always a positive number.
Thus, from equation (X),
The rate would always be a positive.
(iv) The length of the ladder is constant, so, the resultant change would be constant.
i.e. x = increases ⇒ y = decreases
y = decreases ⇒ y = increases
(v) if ladder hit the ground x = 0,
So, from equation (X),
