Final answer:
The acceleration of the crate on the frictionless ramp is 2.38 m/s². When there is a friction force of 1.9 N, the acceleration becomes 5.1 m/s².
Step-by-step explanation:
To find the acceleration of the crate, we need to use Newton's second law, which states that the net force acting on an object is equal to the product of its mass and acceleration. In this case, the net force acting on the crate is the applied force parallel to the incline, which is 7.0 N. The mass of the crate is 1.0 kg.
Using trigonometry, we can find that the component of the force parallel to the incline is 7.0 N * sin(20°), which is approximately 2.38 N. Since there is no friction, this force is also equal to the weight component down the incline. So, we can set up the equation:
2.38 N = 1.0 kg * a,
where a is the acceleration of the crate.
Solving for a, we get a = 2.38 m/s2.
In the case where there is a friction force of 1.9 N, we need to take into account the additional force opposing the motion. The net force now becomes 7.0 N - 1.9 N = 5.1 N. Using the same equation with the new net force, we get a = 5.1 N / 1.0 kg = 5.1 m/s2.