Force/Vector Question: A box is being pulled by two ropes...

[lual0209]

Please could you help with the following question:

1. A box is being pulled by means of two ropes. One rope exerts 60 pounds of force at 16 degrees above the horizontal. The other rope exerts 54 pounds of force at 26 degrees below the horizontal. Find the direction and magnitude of the resultant of the two forces.

Is this?:

AB = 60 sin 16 degrees = 16.53824135 pounds upwards.

AC = 54 sin 26 degrees = 23.67204193 pounds downwards.

Therefore AB + AC = 40.21028328 pounds = 40 pounds horizontally.

Thank you.

 

[Deleted member 4993]

Re: Force/Vector Question

Please could you help with the following question:

1. A box is being pulled by means of two ropes. One rope exerts 60 pounds of force at 16 degrees above the horizontal. The other rope exerts 54 pounds of force at 26 degrees below the horizontal. Find the direction and magnitude of the resultant of the two forces.

Is this?:<<< Incorrect

AB = 60 sin 16 degrees = 16.53824135 pounds upwards.

AC = 54 sin 26 degrees = 23.67204193 pounds downwards.

Therefore AB + AC = 40.21028328 pounds = 40 pounds horizontally.<<< How are two vertical components added together gives you horizontal component?

Thank you.

What methods of vector addition have you been taught?

 

[lual0209]

Re: Force/Vector Question

Please could you help with the following question:

1. A box is being pulled by means of two ropes. One rope exerts 60 pounds of force at 16 degrees above the horizontal. The other rope exerts 54 pounds of force at 26 degrees below the horizontal. Find the direction and magnitude of the resultant of the two forces.

Is this?:<<< Incorrect

AB = 60 sin 16 degrees = 16.53824135 pounds upwards.

AC = 54 sin 26 degrees = 23.67204193 pounds downwards.

Therefore AB + AC = 40.21028328 pounds = 40 pounds horizontally.<<< How are two vertical components added together gives you horizontal component?

Thank you.

What methods of vector addition have you been taught?

Well, I know that the sum of v = square root of a^2 + b^2; v + w = (a,b) + (c, d) = (a + c, b + d); and kv = k (a, b) = (ka, kb).

 

[Deleted member 4993]

Re: Force/Vector Question

DUPLICATE POST

viewtopic.php?f=10&t=34310

Well, I know that the sum of v = square root of a^2 + b^2; v + w = (a,b) + (c, d) = (a + c, b + d); and kv = k (a, b) = (ka, kb).

v + w = (a,b) + (c, d) = (a + c, b + d);

You would have to use this method.

What does a,b,c & d mean in this context?

 

[lual0209]

Re: Force/Vector Question

DUPLICATE POST

viewtopic.php?f=10&t=34310

Well, I know that the sum of v = square root of a^2 + b^2; v + w = (a,b) + (c, d) = (a + c, b + d); and kv = k (a, b) = (ka, kb).

v + w = (a,b) + (c, d) = (a + c, b + d);

You would have to use this method.

What does a,b,c & d mean in this context?

Thank you Subhotosh. Apologies for the duplicate post. Is this right?

AB = 60 cos16 degrees i + 60 sin16 degrees j = 57.7 i + 16.5 j.

AD = 54 cos-26 degrees i + 54 sin-26 degrees j = 48.5 i + (-23.7) j.

AC = 57.7 + 48.5 = 106.2 i, 16.5 + (-23.7) = -7.2 j.

Sum of AC = square root of (106.2)^2 + (-7.2)^2 = 106 pounds.

beta = inverse tan (-7.2/106.2) = -3.9 degrees.

Therefore, answer = 106 pounds at 3.9 degrees below the horizontal.

 

[lual0209]

DUPLICATE POST

viewtopic.php?f=10&t=34310

Well, I know that the sum of v = square root of a^2 + b^2; v + w = (a,b) + (c, d) = (a + c, b + d); and kv = k (a, b) = (ka, kb).

v + w = (a,b) + (c, d) = (a + c, b + d);

You would have to use this method.

What does a,b,c & d mean in this context?

Thank you Subhotosh. Apologies for the duplicate post. Is this right?

AB = 60 cos16 degrees i + 60 sin16 degrees j = 57.7 i + 16.5 j.

AD = 54 cos-26 degrees i + 54 sin-26 degrees j = 48.5 i + (-23.7) j.

AC = 57.7 + 48.5 = 106.2 i, 16.5 + (-23.7) = -7.2 j.

Sum of AC = square root of (106.2)^2 + (-7.2)^2 = 106 pounds.

beta = inverse tan (-7.2/106.2) = -3.9 degrees.

Therefore, answer = 106 pounds at 3.9 degrees below the horizontal.

Or more accurately (with less rounding): 106.4 pounds at 3.8 degrees below the horizontal.

 

[Deleted member 4993]

Re: Force/Vector Question

DUPLICATE POST

viewtopic.php?f=10&t=34310

Well, I know that the sum of v = square root of a^2 + b^2; v + w = (a,b) + (c, d) = (a + c, b + d); and kv = k (a, b) = (ka, kb).

v + w = (a,b) + (c, d) = (a + c, b + d);

You would have to use this method.

What does a,b,c & d mean in this context?

<<<< Looks good to me

Thank you Subhotosh. Apologies for the duplicate post. Is this right?

AB = 60 cos16 degrees i + 60 sin16 degrees j = 57.7 i + 16.5 j.

AD = 54 cos-26 degrees i + 54 sin-26 degrees j = 48.5 i + (-23.7) j.

AC = 57.7 + 48.5 = 106.2 i, 16.5 + (-23.7) = -7.2 j.

Sum of AC = square root of (106.2)^2 + (-7.2)^2 = 106 pounds.

beta = inverse tan (-7.2/106.2) = -3.9 degrees.

Therefore, answer = 106 pounds at 3.9 degrees below the horizontal.