A spring balance has a maximum reading of 10N and the length of the calibrated scale is 20cm.a rectangular metal block measuring 10cm by 2cm is hung on the balance and stretches the spring by 15cm.calculate ,the weight of the block and the mass of the block
W = 15/20 * 10 = 7.5 N
m = W/g = 7.5/9.81 = 0.765 kg
Well, the situation sounds imbalanced! Let's get into some calculations.
First, let's find the weight of the block. We know that weight (W) is equal to mass (m) times gravitational acceleration (g). Since the block is at rest, its weight will be balanced by the tension in the spring.
Given that the maximum reading on the spring balance is 10N, which corresponds to 15cm of stretch, we can set up a proportion to find the constant of the spring.
10N corresponds to 15cm of stretch, so:
10N / 15cm = x / 20cm
Solving for x, we find that x = 13.33N. So, for every centimeter of stretch, the spring balance reads 0.6667N.
Now, let's calculate the weight of the block. The block causes a stretch of 15cm on the spring balance, which means the reading on the scale would be:
15cm x 0.6667N/cm = 10N
Since the weight of the block is balanced by the tension in the spring, the weight of the block is 10N.
Next, let's find the mass of the block. Using the formula W = m * g, rearranging it to m = W / g, we can calculate the mass.
Given that the weight is 10N and standard gravitational acceleration is around 9.8m/s^2, we can substitute these values into the equation:
m = 10N / 9.8m/s^2 ≈ 1.02 kg
So, the weight of the block is 10N, and the mass of the block is approximately 1.02 kg. Now, that's some heavy metal!
To calculate the weight of the block, we can use the formula:
Weight = Force = mass * gravity
where gravity is approximately 9.8 m/s^2.
First, let's find the force applied to the spring, using the given information.
1. Determine the change in length of the spring:
Change in length = stretched length - original length
Change in length = 15 cm - 0 cm
Change in length = 15 cm
2. Convert the change in length from cm to m:
Change in length = 15 cm * 0.01 m/cm
Change in length = 0.15 m
3. Calculate the force applied to the spring:
Force = spring constant * change in length
Since we have not been given the spring constant of the spring balance, we cannot determine the force and, therefore, the weight of the block accurately.
To calculate the weight of the block, we need to use the formula:
Weight = Mass * Gravitational acceleration
Let's begin by calculating the weight:
Step 1: Convert the length of the calibrated scale from centimeters to meters:
Length = 20cm = 0.2m
Step 2: Calculate the force applied by the spring balance using Hooke's Law:
Force = Spring Constant * Extension
Since the spring balance has a maximum reading of 10N and it stretched by 15cm, we have:
Force = 10N
Extension = 15cm = 0.15m
So, the force applied by the spring balance is 10N.
Step 3: Calculate the weight of the block:
Weight = Force
Since the weight and the force applied by the spring balance are the same, the weight of the block is 10N.
Now let's calculate the mass of the block:
Step 4: Use the equation Weight = Mass * Gravitational acceleration to calculate the mass:
Weight = Mass * Gravitational acceleration
Rearranging the equation, we get:
Mass = Weight / Gravitational acceleration
Substitute the values:
Mass = 10N / 9.8 m/s^2
Mass ≈ 1.02 kg (rounded to two decimal places)
Therefore, the weight of the block is 10 Newtons, and the mass of the block is approximately 1.02 kilograms.